Question

solve the linear system using elimination. your answer is an ordered pair (x, y).
2x + y = 10
5x - y = 18
options: (8, 4), (4, 2), (2, 4), (4, 8)

Explanation:

Step1: Write the system of equations

We have the system:

$$\begin{cases} 2x + y = 10 \\ 5x - y = 18 \end{cases}$$

Step2: Eliminate \(y\) by adding the two equations

Add the left - hand sides and the right - hand sides of the two equations:
\((2x + y)+(5x - y)=10 + 18\)
Simplify the left - hand side: \(2x+y + 5x-y=7x\), and the right - hand side: \(10 + 18 = 28\). So we get the equation \(7x=28\).

Step3: Solve for \(x\)

Divide both sides of the equation \(7x = 28\) by 7: \(x=\frac{28}{7}=4\).

Step4: Substitute \(x = 4\) into the first equation to solve for \(y\)

Substitute \(x = 4\) into \(2x + y=10\): \(2\times4+y = 10\), which simplifies to \(8 + y=10\).
Subtract 8 from both sides: \(y=10 - 8=2\).

Answer:

\((4,2)\)